Exam 5: The Standard Deviation As a Ruler and the Normal Model

Although most of us buy milk by the quart or gallon, farmers measure daily production in pounds.Guernsey cows average 39 pounds of milk a day with a standard deviation of 8 pounds.For Jerseys the mean daily production is 43 pounds with a standard deviation of 5 pounds.When being shown at a state fair a champion Guernsey and a champion Jersey each gave 54 pounds of milk.Which cow's milk production was more remarkable? Explain.

The time it takes to process phone orders in a small florist/gift shop is normally distributed With a mean of 6 minutes and a standard deviation of 1.24 minutes.What cutoff values Would separate the 16% of orders that take the least time to process?

A company's manufacturing process uses 500 gallons of water at a time.A "scrubbing" Machine then removes most of a chemical pollutant before pumping the water into a nearby Lake .To meet federal regulations the treated water must not contain more than 80 parts per Million (ppm) of the chemical.Because a fine is charged if regulations are not met, the Company sets the machine to attain an average of 75 ppm in the treated water.The Machine's output can be described by a normal model with standard deviation 4.2 ppm.What Percent of the batches of water discharged exceed the 80 ppm standard?

A vendor offers various t-shirts for sale on an Internet commerce site.Some of his t-shirts sell quite well, others have yet to find an interested customer.The summary 23 Median 15 Min 0 Q1 3 Q3 21 Max 82 sd 7.84 statistics are listed on right, based on the number of sales per month for each of 80 different t-shirt designs. A.What is the shape of this distribution? Explain how you know. B.If the vendor spends $2 per t-shirt in shipping costs, what is his average monthly costs per t-shirt sold? What is the standard deviation of this cost? Show work. c.As time passes, the vendor has simplified his profit calculation.He estimates that he has monthly flat costs of $35, with a gain of $3.50 per t-shirt sold.What is the median of his profit? The IQR? d.What are the mean and standard deviation of his profit? e.What is more appropriate in this case: using mean and standard deviation, or using median and IQR?

A soft drink dispenser can be adjusted to deliver any fixed number of centiliters.If the Machine is operating with a standard deviation in delivery equal to 0.3 centiliter, what should Be the mean setting so that a 12-centilitre cup will overflow less than 1% of the time? Assume a normal distribution for centiliters delivered.

Suppose that the weights of vans delivering goods to inner city shops are normally Distributed.If 70% of the vans weigh more than 1200 kg, and 80% weigh more than 1000 kg, What are the mean and standard deviation for the weights of vans serving the inner city (round to tens)?

Based on data collected from its production processes, Crosstiles InC.determines that the Breaking strength of its most popular porcelain tile is normally distributed with a mean of 400 pounds per square inch and a standard deviation of 12.5 pounds per square inch.Based On the 68-95-99.7 Rule, about what percent of its popular porcelain tile will have breaking Strengths between 375 and 425 pounds per square inch?

A small flower shop takes orders by phone and then one of the staff florists is assigned to Prepare the arrangement.The time it takes to process phone orders is normally distributed With a mean of 6 minutes and a standard deviation of 2.5 minutes.The time it takes for an Arrangement to be completed is normally distributed with a mean of 35 minutes and a Standard deviation of 8.6 minutes.What is the standard deviation for the total time to process a phone order and complete the floral arrangement at this flower shop (assuming times are Independent)?

Students taking an intro stats class reported the number of credit hours that they were taking that quarter.Summary statistics are shown in the table. 16.65 s 2.96 5 Q1 15 median 16 Q3 19 28 A.Suppose that the college charges $73 per credit hour plus a flat student fee of $35 per quarter.For example, a student taking 12 credit hours would pay $35 + $73(12) = $911 for that quarter. i.What is the mean fee paid? ii.What is the standard deviation for the fees paid? iii.What is the median fee paid? iv.What is the IQR for the fees paid? B.Twenty-eight credit hours seems like a lot.Would you consider 28 credit hours to be unusually high? Explain.